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Optical Forces in Nanowire Pairs and Metamaterials Optical forces in nanowire pairs and metamaterials Rongkuo Zhao,1,2 Philippe Tassin,1,3 Thomas Koschny,1,4 and Costas M. Soukoulis1,4,∗ 1Ames Laboratory—U.S. DOE, and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA 2Applied Optics Beijing Area Major Laboratory, Department of Physics, Beijing Normal University, Beijing 100875, China 3Department of Applied Physics and Photonics, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussel, Belgium 4Institute of Electronic Structure and Lasers (IESL), FORTH, and Department of Material Science and Technology, University of Crete, 71110 Heraklion, Crete, Greece *[email protected] Abstract: We study the optical force arising when isolated gold nanowire pairs and metamaterials with a gold nanowire pair in the unit cell are illu- minated with laser radiation. Firstly, we show that isolated nanowire pairs are subject to much stronger optical forces than nanospheres due to their stronger electric and magnetic dipole resonances. We also investigate the properties of the optical force as a function of the length of the nanowires and of the distance between the nanowires. Secondly, we study the optical force in a metamaterial that consists of a periodic array of nanowire pairs. We show that the ratio of the size of the unit cell to the length of the nanowires determines whether the electric dipole resonance leads to an attractive or a repulsive force, and we present the underlying physical mechanism for this effect. © 2010 Optical Society of America OCIS codes: (160.3918) Metamaterials; (260.2110) Electromagnetic optics. References and links 1. J. C. Maxwell, A Treatise on Electricity and Magnetism (Clarendon Press, Oxford, 1873). 2. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962). 3. S. Chu, “Nobel lecture: The manipulation of neutral particles,” Rev. Mod. Phys. 70, 685–706 (1998). 4. C. Cohen-Tannoudji, “Nobel lecture: Manipulating atoms with photons,” Rev. Mod. Phys. 70, 707–719 (1998). 5. W. D. Phillips, “Nobel lecture: Laser cooling and trapping of neutral atoms,” Rev. Mod. Phys. 70, 721–741 (1998). 6. M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature (London) 456, 480–484 (2008). 7. D. Van Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force,” Nat. Photonics 4, 211–217 (2010). 8. M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Opt. Lett. 30, 3042–3044 (2005). 9. G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature (London) 462, 633–636 (2009). 10. T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: Back-action at the mesoscale,” Science 321, 1172– 1176 (2008). 11. A. J. Hallock, P. L. Redmond, and L. E. Brus, “Optical forces between metallic particles,” Proc. Natl. Acad. Sci. U.S.A. 102, 1280–1284 (2005). 12. P. Chu and D. L. Mills, “Laser-induced forces in metallic nanosystems: The role of plasmon resonances,” Phys. Rev. Lett. 99, 127401 (2007). #135312 - $15.00 USD Received 22 Sep 2010; revised 9 Nov 2010; accepted 12 Nov 2010; published 23 Nov 2010 (C) 2010 OSA 6 December 2010 / Vol. 18, No. 25 / OPTICS EXPRESS 25665 13. C. Rockstuhl and H. P. Herzig, “Wavelength-dependent optical force on elliptical silver cylinders at plasmon resonance,” Opt. Lett. 29, 2181–2183 (2004). 14. K. Halterman, J. M. Elson, and S. Singh, “Plasmonic resonances and electromagnetic forces between coupled silver nanowires,” Phys. Rev. B 72, 075429 (2005). 15. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001). 16. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and µ,” Sov. Phys. Usp. 10, 509–514 (1968). 17. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin wire structures,” J. Phys. Condens. Matter 10, 4785–4809 (1998). 18. D. R. Smith, W. J. Padilla, D. C. Vier, D. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultane- ously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000). 19. N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the electric resonance of split-ring resonators,” Appl. Phys. Lett. 84, 2943–2945 (2004). 20. T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Effective medium theory of left-handed materials,” Phys. Rev. Lett. 93, 107402 (2004). 21. J. Garcia-Garcia, F. Martin, J. D. Baena, R. Marques, and L. Jelink, “On the resonances and polarizabilities of split-ring resonators,” J. Appl. Phys. 98, 033103 (2005). 22. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative index metamaterials,” Phys. Rev. Lett. 95, 137404 (2005). 23. G. Dolling, C. Enkrich, M. Wegener, and C. M. Soukoulis, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett. 30, 3198–3200 (2005). 24. V. M. Shalaev, W. S. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30, 3356–3358 (2005). 25. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). 26. M. N’Gom, J. Ringnalda, J. F. Mansfield, A. Agarwal, N. Kotov, N. J. Zaluzec, and T. B. Norris, “Single particle plasmon spectroscopy of silver nanowires and gold nanorods,” Nano Lett. 8, 3200–3204 (2008). 27. H.-S. Park, A. Agarwal, N. A. Kotov, and O. D. Lavrentovich, “Controllable side-by-side and end-to-end assem- bly of Au nanorods by lyotropic chromonic materials,” Langmuir 24, 13833–13837 (2008). 28. J. Zhou, E. N. Economou, T. Koschny, and C. M. Soukoulis, “Unifying approach to left-handed material design,” Opt. Lett. 31, 3620–3622 (2006). 29. P. Gay-Balmaz and O. J. F. Martin, “Electromagnetic resonances in individual and coupled split-ring resonators,” J. Appl. Phys. 92, 2929–2936 (2002). 30. R. S. Penciu, K. Aydin, M. Kafesaki, T. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, “Multi-gap individual and coupled split-ring resonator structures,” Opt. Express 16, 18131–18144 (2008). 31. P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Low loss metamaterials based on classical electromagnetically induced transparency,” Phys. Rev. Lett. 102, 053901 (2009). 32. P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Planar designs for electromagnetically induced transparency in metamaterials,” Opt. Express 17, 5595–5605 (2009). 33. N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, “A metamaterial analog of electromagneti- cally induced transparency,” Phys. Rev. Lett. 101, 253903 (2008). 34. N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8, 758–762 (2009). 1. Introduction The idea that electromagnetic radiation carries linear momentum goes back to James Clark Maxwell and his contemporaries [1]; it is indeed the only way to reconcile Maxwell’s equa- tions with the principle of conservation of linear momentum [2]. Transfer of linear momentum from electromagnetic radiation to matter particles happens in the well-known phenomenon of radiation pressure, which is at least partially responsible for the tail of comets pointing away from the sun and is used in laser cooling to cool down atoms to temperatures close to the ab- solute zero [3–5]. Recently, it has been proposed to harness optical forces, i.e., the forces that arise when linear momentum is transferred from photons to matter, in micro- and nanophotonic systems [6, 7]. Optical forces are commonly classified as either gradient or scattering forces. The gradient force is an optical force that is perpendicular to the propagation direction of the excitation electromagnetic field and is well known for its use in optical tweezers, where strong laser #135312 - $15.00 USD Received 22 Sep 2010; revised 9 Nov 2010; accepted 12 Nov 2010; published 23 Nov 2010 (C) 2010 OSA 6 December 2010 / Vol. 18, No. 25 / OPTICS EXPRESS 25666 beams generate a piconewton force that is used for the manipulation of small dielectric particles, including DNA, enzymes, and biological entities such as cells and bacteria. The physics of optical tweezers can be understood by recognizing that a dielectric particle can lower its energy by moving towards a region with higher field intensity [2]. More recently, researchers have exploited the gradient optical force for all-optical actuation of nanomechanical systems. The typical setup consists of two suspended waveguides close to each other; each of the waveguides sits in the exponential tail of the other waveguide’s mode and will therefore be subjected to an optical force of a few piconewtons per milliwatt of optical power [6, 8]. The force can be enhanced using various types of optical resonators, such as ring resonators, up to a few nanonewtons per milliwatt [9]. As opposed to the gradient force, the scattering optical force imparts momentum parallel to the propagation direction of the excitation field. It has been studied extensively in the field of cavity optomechanics. The typical setup in this case consist of an optical cavity of which one mirror is free to oscillate as a mechanical harmonic oscillator. It has been demonstrated theoretically and experimentally that the optical force on the mirror and the resulting coupling between the optical modes and the mechanical motion leads to peculiar effects such as amplifi- cation and cooling of the mechanical oscillator [10].
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